Modules over universal regular rings

Roger Allen Wiegand

Vol. 39 (1971), No. 3, 807–819

DOI: 10.2140/pjm.1971.39.807

Abstract

To each commutive ring R there is associated a certain commutative regular ring R. The ring R is in fact an R-algebra. It is shown that RR is never flat, unless R is itself regular. The functor taking R to R preserves direct limits, and, in certain cases, tensor products. It is shown that if R is weakly noetherian then the global dimension of R less than or equal to the Krull dimension of R. Necessary and sufficient conditions that R be a quotient ring of R are determined.

Mathematical Subject Classification 2000

Primary: 13C10

Milestones

Received: 4 December 1970

Revised: 9 July 1971

Published: 1 December 1971